you pick a card at random, put it back, and then pick another card at random. what is the probability of…

you pick a card at random, put it back, and then pick another card at random. what is the probability of picking a 7 and then picking a 6? write your answer as a fraction or whole number.

you pick a card at random, put it back, and then pick another card at random. what is the probability of picking a 7 and then picking a 6? write your answer as a fraction or whole number.

Answer

Explanation:

Step1: Calculate probability of picking 7 first

There are 3 cards, so the probability of picking a 7 on the first - draw is $\frac{1}{3}$.

Step2: Calculate probability of picking 6 second

Since the card is put back, there are still 3 cards. The probability of picking a 6 on the second - draw is $\frac{1}{3}$.

Step3: Calculate the joint probability

For independent events, the joint probability is the product of the individual probabilities. So the probability of picking a 7 and then a 6 is $\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$